In the Dirac canonical theory [1]} constraints may be distinguished as either first or second class. Briefly stated, a constraint is first class when its Poisson bracket with all other constraints vanishes weakly.More specifically, for a set of \(N\)  constraints \(\tilde{C}_{i}\)  (\(i = 1, \cdots , N\) ), each of which weakly vanish, i.e. \(\tilde{C}_{i}\approx 0\) , a constraint is first class when its Poisson bracket with all other constraints vanishes weakly
\(\left\lbrace \tilde{C}_{i},\tilde{C}_{j} \right\rbrace \approx 0~.\) 
This therefore implies that the Poisson bracket of two first class constraints must itself be strongly equal to a linear combination of constraints such that
\(\left\lbrace \tilde{C}_{i},\tilde{C}_{j} \right\rbrace  = \sum _{k}\alpha _{k}\tilde{C}_{k}~.\) 
 Here we have just one constraint
\(\left\lbrace \tilde{N},\tilde{N} \right\rbrace  = 0~,\) 
